A larky, anarchic life force runs through “American Hustle,” David O. Russell’s screwball homage to the strivers and connivers who wreak playful havoc with what could easily have been a straight-up, if antic, FBI procedural.

Notionally based on the 1978 Abscam investigation, wherein an FBI sting used fake Arab sheiks to ferret out corruption within the ranks of Congress and local jurisdictions, “American Hustle” cheerfully jettisons any pretense of historical accuracy or journalistic shoe-leather. Such carefully footnoted Washington tableaux as “Argo,” “Zero Dark Thirty” and “Lincoln” are so last year, literally and figuratively: The tag­line at the beginning of “American Hustle” reads proudly, “Some of this actually happened.”

In other words: Permission granted to leave Wikipedia behind and allow yourselves to be entertained by this rollicking, sometimes unhinged shaggy-dog tale.

The film opens on Christian Bale, unrecognizable behind a prodigiously flabby belly, meticulously arranging a toupee and comb-over while the New York news radio station WINS chatters in the background. It’s an otherwise silent masterpiece of real-time self-invention, which isn’t subtext as much as the text of Russell’s fanciful story about characters who construct identities out of whole cloth, not just to deceive but to give themselves the existential juice it takes to get through another day.

Bale plays con artist Irving Rosenfeld, a Bronx-born sharpie who deals in fake loans and forged art, using a dry-cleaning business to launder his dirty money. When Irving meets Sydney (Amy Adams), they find immediate fellowship in worshipping Duke Ellington and harboring hearts full of larceny. It’s as if two illusions recognize, reach out and touch one another at their deepest, most dissembling cores.

Once Irving and Sydney cross paths with an ambitious FBI agent named Richie DiMaso (Bradley Cooper), the game is afoot, and the three embark on an increasingly elaborate folly during which their shifting personas and motivations come into increasingly dubious question. Russell expertly peels back the layers of the characters’ “real” lives, doling out information in stingy, delicious dollops. As he’s done in “The Fighter” and “Silver Linings Playbook,” Russell follows his rogues’ gallery closely, his fluid, discreetly observant Steadicam following just behind or alongside — an intimacy that makes it all the more startling when a fact emerges that fundamentally alters our understanding of who we thought they were.

Bale, Adams and Cooper develop a credible, explosively volatile chemistry in “American Hustle,” and Bale is particularly heroic in his portrayal of a blubbery white whale of a man trying to shake that last harpoon. But the film is filled with terrific supporting performances as well, from Jeremy Renner as a pompadoured New Jersey mayor and Louis C.K. as DiMaso’s beleaguered superior at the FBI to that brand of cinematic secret sauce known as Jennifer Lawrence, whose voluptuous, daffy 1970s housewife (“the Picasso of passive-aggressive karate,” as another character describes her) possesses equal parts unstudied incandescence and Loki-like derangement.

Russell is so entranced by his characters that he films them like the stars of an old-school musical, swirling across Park Avenue, lip-syncing to each other on the dance floor, or to Paul McCartney’s “Live and Let Die” directly to the camera. And he’s as entranced by the material culture of this world as he is by the people: From the ubiquitous corner ficus tree to mirrored wallpaper, every visual cue is as expressive of its era as the Halston dresses that the female characters drape over their bodies, with nary a Maidenform in sight.

At times, Russell’s exuberance gets the better of him: He’s prone to over-relying on music to sell a scene, and the reference-upon-reference layering can be exhausting. (In the course of just a minute or two in one crucial sequence, we hear Elton John, Santana, an Arabic version of “White Rabbit” and the Bee Gees in quick succession.) But if only as a period piece — and, incidentally, a fitting next-decade New York bookend to “Inside Llewyn Davis,” also opening Friday — “American Hustle” is a joy to watch, its infectious brio giving the audience a time-warp contact high.

The warmth that courses through “American Hustle” makes it irresistible, with Russell’s affection for his characters and his sharp-eyed evocation of their recessionary times, honoring their struggle, however dishonest, rather than denigrating it. If his idealism strikes some viewers as unearned, it offers a bracing counterpoint to the unremitting cynicism of the upcoming “Wolf of Wall Street,” in which greed is the same operating principle, albeit with no reassuring third-act redemption.

The Martin Scorsese movie that “American Hustle” most recalls is “Goodfellas,” which was propelled by the same jittery expansiveness but was willing to go to exponentially darker places. Russell is content to keep it light, preferring to see even his most cracked characters as dreamers in search of the genuine article, whether in love, friendship or civic virtue. “American Hustle” may have taken its inspiration from the art of the steal, but it has a heart of pure, if slightly tarnished, gold.

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Comments our editors find particularly useful or relevant are displayed in Top Comments, as are comments by users with these badges: . Replies to those posts appear here, as well as posts by staff writers.